Internal problem ID [8149]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 674.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }-4 y^{\prime } x^{2}+\left (2 x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(4*x^2*diff(y(x),x$2)-4*x^2*diff(y(x),x)+(1+2*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {x}+c_{2} \sqrt {x}\, \operatorname {Ei}_{1}\left (-x \right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 19
DSolve[4*x^2*y''[x]-4*x^2*y'[x]+(1+2*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x} (c_2 \operatorname {ExpIntegralEi}(x)+c_1) \]